Inequalities I - Challenging

Question 1: Solve the equation:

\frac{{(\sqrt{x})}^{2} + 6 - x^{2}}{x - 2} \leq 0

A

x \in [0; 2) \cup [3; + \infty)

B

x \in [0; 2] \cup [3; + \infty)

C

x \in [0; 2)

D

x \in [3; + \infty)

Question 2: Solve the inequality:

|\frac{1}{x - 2}| > 1

for

x > 3

A

x \in (2; 3)

B

x = 3

C

x \in \emptyset

D

x \in [2; 3]

Question 3: Solve the inequality:

\frac{x^{2} - 4 x + 3}{x^{2} - 8 x + 7} < 0

A

x \in (3; 7)

B

x \in [3; 7)

C

x \in (3; 7]

D

x \in [3; 7]

Question 4: Solve the inequality:

\frac{1}{|x| + 3} < 1

A

x \in (- 2; 2)

B

x \in ℝ

C

x \in (2; + \infty)

D

x \in (0; + \infty)

Question 5: Solve the inequality:

\frac{x - 1}{x + 1} < x

A

x \in (- 1; 1)

B

x \in (- 3; - 2) \cup (- 1; + \infty)

C

x \in (- 1; + \infty)

D

x \in [- 1; + \infty)

Question 6: Solve the inequality:

\sqrt{x^{2} - 7 x + 12} < x

A

x \in (- \infty; 3] \cup [4; + \infty)

B

x \in (\frac{12}{7}; 3) \cup (4; + \infty)

C

x \in (\frac{12}{7}; + \infty)

D

x \in (\frac{12}{7}; 3] \cup [4; + \infty)

Question 7: Solve the inequality:

\frac{1}{x - 1} < \frac{2}{x - 2}

A

x \in (1; 2)

B

x \in [0; 1) \cup (2; + \infty)

C

x \in (0; 1) \cup (2; + \infty)

D

x \in (2; + \infty)

Question 8: Solve the inequality:

\frac{x^{2} - 4 x - 5}{x^{2} - 11 x + 30} > 0

A

x \in (6; + \infty)

B

x \in (- \infty; - 1)

C

x \in (- \infty; - 1) \cup (6; + \infty)

D

x \in (- 1; 5) \cup (6; + \infty)

Question 9: Solve the inequality:

\frac{x^{2} - 2 x + 1}{x - 5} \leq 0

A

x \in [1; 5)

B

x \in (- \infty; 5]

C

x \in (- \infty; 1]

D

x \in (- \infty; 5)

Question 10: Solve the inequality:

|x^{2} - 4 x + 2| \leq 2

A

x \in [1; 4]

B

x \in (0; 4)

C

x \in (0; 4]

D

x \in [0; 4]

Test: Inequalities I - Challenging

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